Average Error: 0.6 → 0.4
Time: 16.6s
Precision: binary64
\[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
↓
\[1 - \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}}}} \cdot \frac{\sqrt[3]{1}}{\frac{\sqrt[3]{y - z}}{\frac{\sqrt[3]{x}}{\sqrt[3]{y - t}}}}\]
1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}
↓
1 - \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}}}} \cdot \frac{\sqrt[3]{1}}{\frac{\sqrt[3]{y - z}}{\frac{\sqrt[3]{x}}{\sqrt[3]{y - t}}}}
(FPCore (x y z t) :precision binary64 (- 1.0 (/ x (* (- y z) (- y t)))))
↓
(FPCore (x y z t)
 :precision binary64
 (-
  1.0
  (*
   (/
    (* (cbrt 1.0) (cbrt 1.0))
    (/
     (* (cbrt (- y z)) (cbrt (- y z)))
     (/ (* (cbrt x) (cbrt x)) (* (cbrt (- y t)) (cbrt (- y t))))))
   (/ (cbrt 1.0) (/ (cbrt (- y z)) (/ (cbrt x) (cbrt (- y t))))))))
double code(double x, double y, double z, double t) {
	return 1.0 - (x / ((y - z) * (y - t)));
}
↓
double code(double x, double y, double z, double t) {
	return 1.0 - (((cbrt(1.0) * cbrt(1.0)) / ((cbrt(y - z) * cbrt(y - z)) / ((cbrt(x) * cbrt(x)) / (cbrt(y - t) * cbrt(y - t))))) * (cbrt(1.0) / (cbrt(y - z) / (cbrt(x) / cbrt(y - t)))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.6

    \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\]
  2. Using strategy rm

  3. Applied clear-num_binary64_79200.7

    \[\leadsto 1 - \color{blue}{\frac{1}{\frac{\left(y - z\right) \cdot \left(y - t\right)}{x}}}\]

  4. Simplified1.1

    \[\leadsto 1 - \frac{1}{\color{blue}{\frac{y - z}{\frac{x}{y - t}}}}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt_binary64_79561.3

    \[\leadsto 1 - \frac{1}{\frac{y - z}{\frac{x}{\color{blue}{\left(\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}\right) \cdot \sqrt[3]{y - t}}}}}\]

  7. Applied add-cube-cbrt_binary64_79561.3

    \[\leadsto 1 - \frac{1}{\frac{y - z}{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}\right) \cdot \sqrt[3]{y - t}}}}\]

  8. Applied times-frac_binary64_79271.3

    \[\leadsto 1 - \frac{1}{\frac{y - z}{\color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y - t}}}}}\]

  9. Applied add-cube-cbrt_binary64_79561.4

    \[\leadsto 1 - \frac{1}{\frac{\color{blue}{\left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) \cdot \sqrt[3]{y - z}}}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y - t}}}}\]

  10. Applied times-frac_binary64_79270.4

    \[\leadsto 1 - \frac{1}{\color{blue}{\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}}} \cdot \frac{\sqrt[3]{y - z}}{\frac{\sqrt[3]{x}}{\sqrt[3]{y - t}}}}}\]

  11. Applied add-cube-cbrt_binary64_79560.4

    \[\leadsto 1 - \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}}} \cdot \frac{\sqrt[3]{y - z}}{\frac{\sqrt[3]{x}}{\sqrt[3]{y - t}}}}\]

  12. Applied times-frac_binary64_79270.4

    \[\leadsto 1 - \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}}}} \cdot \frac{\sqrt[3]{1}}{\frac{\sqrt[3]{y - z}}{\frac{\sqrt[3]{x}}{\sqrt[3]{y - t}}}}}\]

  13. Final simplification0.4

    \[\leadsto 1 - \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - t} \cdot \sqrt[3]{y - t}}}} \cdot \frac{\sqrt[3]{1}}{\frac{\sqrt[3]{y - z}}{\frac{\sqrt[3]{x}}{\sqrt[3]{y - t}}}}\]

Reproduce

herbie shell --seed 2021098 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, A"
  :precision binary64
  (- 1.0 (/ x (* (- y z) (- y t)))))